Optimize the FOR loop

I am learning to optimize the following nested FOR loop, any comments are appreciated,

    x=[537 558 583 606 631 655 666 700 722 799 823 847];
    y=[48 216 384 552 720 888 1056];

    z = zeros(1,numel(x));

    for j = 1:numel(x)
        for i = 1:numel(y)
            if(x(j) <= y(i) )
                z(j) = i;
                break;
            end
        end
    end

    %ans 
    %z = [4 5 5 5 5 5 5 5 6 6 6 6]

[Ryan]

To clarify: For each value in 'x', you're trying to locate the position of the first value in 'y' that is greater than the value in 'x' and then return that position in a vector 'z'?

[Sam]

yes

Answer 1

[Sean de Wolski]

If you can guarantee that the is at least one occurence of x(:) <y (:) then this will work:

x=[537 558 583 606 631 655 666 700 722 799 823 847];
y=[48 216 384 552 720 888 1056];
[~,z] = max(bsxfun(@le,x,y'),[],1)

[Ryan]

I have never used arrayfun or cellfun or bsxfun before and am trying to understand them and have two questions about this solution:

1. Why do you need to transpose y?
2. Is the ~ used to not waste space saving the max values because all you needed was the indices?

[Sean de Wolski]

Hi Ryan,

For your first question,

bsxfun: please see my answer from a long time ago here: http://www.mathworks.com/matlabcentral/answers/16257#answer_22019

cellfun: Apply some function each cell. Can be useful sometimes for simple calculations, e.g: How many elements in each cell?

cellfun(@numel,C);

For any complicated function, just us e a for-loop, it'll likely be faster.

arrayfun: personal opinion is that it is confusing and slow and should be avoided.

Second question: exactly!

[Tom]

I just compared arrayfun and bsxfun, the latter is a whole order of magnitude faster.

[Ryan]

Thank you Sean and Tom!

Answer 2

[Tom]

It seems what you're trying to is find the first instance of each value of x being less than each value of y. You can do this in using arrayfun:

arrayfun(@(n) find(n<y,1),x)

the first argument is an anonymous function. For each value in x, the find function is used to find the first instance of that x value being less than the y vector.

[Tom]

Seeing what Sean said, this way also only works if there is an occurrence of for all of them- if there isn't then 'UniformOutput' has to be set to false, which means the output will be a cell array.